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Research Article Vol. 3, No. 2 / February 2016 / Optica 151 Surface plasmon resonance for characterization of large-area atomic-layer graphene film HENRI JUSSILA,1,* HE YANG,1 NIKO GRANQVIST,2 AND ZHIPEI SUN1,3 1 Department of Micro- and Nanosciences, Aalto University, Tietotie 3, FI-00076 Espoo, Finland BioNavis Ltd., Elopellontie 3C, 33470 Ylöjärvi, Finland 3 e-mail: [email protected] *Corresponding author: [email protected] 2 Received 31 August 2015; revised 22 December 2015; accepted 22 December 2015 (Doc. ID 249115); published 5 February 2016 Characterization of large-area thin films with atomic-scale resolution is challenging but in great demand for diverse applications (e.g., nanotechnology and sensing). Here, we use the Surface Plasmon Resonance (SPR) method to characterize both the thickness and refractive index of chemical-vapor-deposition (CVD)-grown graphene films. The measured refractive index and extinction coefficient values of the CVD-grown graphene monolayer at 670 nm wavelength are 3.135 and 0.897, respectively. Our results demonstrate that SPR shifts generated by graphene films are large (i.e., ∼1°∕nm), almost tenfold larger than that observed in SPR measurements of organic monolayers. We find that this significantly large SPR shift easily enables the thickness of a large area sample (i.e., ∼mm2 ) to be determined with subnanometer-scale resolution. We show that the SPR method can identify thickness of different graphene layers and give an estimate of ∼0.37 nm for the thickness of the CVD-grown graphene layer, which agrees extremely well with the 0.335 nm reported for layer-to-layer carbon atom distance of graphite crystals. Our results open the avenue to fast and cost-effective simultaneous characterization of various parameters (including thickness and optical constants) of thin films at the atomic-scale resolution. The presented characterization method can be applied both to physical characterizations of various two-dimensional layered materials as well as to the use of these layered materials for biosensing applications as shown earlier, due to the favorable properties of graphene plasmons. © 2016 Optical Society of America OCIS codes: (250.5403) Plasmonics; (160.4236) Nanomaterials; (240.6680) Surface plasmons; (000.2170) Equipment and techniques; (310.3840) Materials and process characterization; (300.6550) Spectroscopy, visible. http://dx.doi.org/10.1364/OPTICA.3.000151 1. INTRODUCTION Currently, graphene and other two-dimensional layered materials are at the center of a significant research effort . Graphene in particular, the first two-dimensional atomic crystal, has attracted a significant amount of interest in the past decade due to its many unique physical properties (e.g., strong field effect with ultrahigh electron mobility [2,3], high thermal conductivity , ultrafast broadband optical response [5,6], and strong mechanical strength and large elasticity ), which enable the realization of numerous photonic and optoelectronic applications such as pulsed lasers [5,8], modulators , photodetectors , and flexible screens . For all these applications, it is crucial to characterize the properties (e.g., refractive index, thickness, etc.) of the used graphene films at both laboratory and mass-production scales. The complex refractive index (RI) of graphene can be measured by multiple methods, including spectroscopic ellipsometry and optical contrast analysis [12–16]. The current state of the art for graphene RI determination, spectroscopic ellipsometry, showed that it is possible to measure the optical constants together with the thickness of graphene . However, in those measurements, the thickness of the graphene flakes given by the fitting procedure 2334-2536/16/020151-08$15/0$15.00 © 2016 Optical Society of America deviated as much as 30%. On the other hand, the value of 0.335 nm for layer-to-layer carbon atom distance is commonly used as a thickness of single-layer graphene in the literature. Typical methods used for thickness characterization include Raman spectroscopy measurements , optical contrast analysis [18–20], and atomic force microscopy (AFM) [21–23]. Despite their well-proven applicability, all these methods possess their own limitations, with Raman being a rather indirect method, optical contrast analysis (typically performed to flakes on silicon/ silicon oxide substrates) requiring certain silicon oxide thicknesses to improve the optical contrast, and AFM systematically giving too large thicknesses for exfoliated flakes. Furthermore, all of these methods gather the information from a rather small measurement area. Thus, there is still a great need for a fast, simple, and costeffective characterization method suitable for the measurement of large-area samples. Surface Plasmon Resonance (SPR) is a surface-sensitive optical analysis technique capable of measuring ultrathin film properties when full angular spectra are measured . While the SPR method is more typically associated with (bio)chemical interaction analysis, the method also shows excellent performance for Research Article characterizing nanoscale thin films , especially with the newly arising multiple-wavelength methods in both wet and dry states [26–28]. SPR is similar to ellipsometry in being a noninvasive optical characterization technique, but SPR uses a noble metal coating on sensors (typically gold) to create a highly sensitive evanescent field at the metal surface, thus creating conditions which are extremely sensitive to small changes in the close vicinity of the surface (∼300 nm). Working with graphene by SPR and several other graphene applications utilizing plasmonics has been demonstrated and reviewed [1,29–40]. In particular, it has been discussed that graphene surfaces on SPR sensors increase the sensor sensitivity; graphene has therefore been used as an alternative chemical platform to the gold coatings [32,38,39]. However, these works [29–40] have shown relatively little interest in using the method to characterize the intrinsic film properties. In this work, we present a simple, noninvasive SPR-based measurement method for characterization of the thickness and complex RI of chemical-vapor-deposition (CVD)-grown graphene films with large area (i.e., ∼mm2 ). The obtained optical information (i.e., RI of 3.135 and extinction coefficient of 0.897) is compared to the values measured by other groups which are commonly used in the literature. We also show that the SPR method easily detects different graphene layer thicknesses and give an estimate of ∼0.37 nm for the thickness of the CVD-grown graphene layer, which agrees extremely well with the reported 0.335 nm for layer-to-layer carbon atom distance of graphite crystals. Furthermore, both of these measured parameters are obtained simultaneously from a single measurement without any a priori information on these parameters. Thus, the presented method can be applied both to graphene physical characterization as well as to the use of graphene in biosensing applications as presented earlier [1,29–40]. 2. SAMPLE FABRICATION AND EXPERIMENTAL METHODS CVD-grown graphene layers were transferred onto SPR sensors composed of optical glass, Cr adhesion layer, plasmonic Au coating, and an additional Al2 O3 thin-film top coating on plasmonic Au coating labeled as Au and Al2 O3 sensors, respectively. CVDgrown graphene layers (fabricated as in Ref. ) were chosen due to their uniformity, which allows us to use a simple wet transfer process in the sample fabrication and prevents the complicated alignment steps which would be required in the SPR measurements of micromechanically exfoliated graphene flakes. The graphene transfer was performed using a standard wet transfer process as follows. First, polymethyl methacrylate (PMMA) polymer was coated onto the surface of CVD-grown graphene for protection. Afterward, copper substrate on which the graphene had been grown was etched using ammonium peroxydisulfate. Then, PMMA-coated graphene film was transferred onto the SPR sensor. In order to get rid of all the moisture, sensors were then heated on a hotplate for 10 min at 150°C. Finally, the protective PMMA film was removed after dissolving the sensors in acetone. The transfer process was repeated three times, and therefore the samples studied in this work were N layers of CVD-grown graphene (N 1, 2, and 3), with all of the different graphene layers originating from the same growth run. Figure 1(a) shows an optical image taken from one of the characterized samples. The sensor cross-section is shown in the inset of Fig. 1(a). Two surface Vol. 3, No. 2 / February 2016 / Optica 152 Fig. 1. (a) Optical image of one of the studied Al2 O3 sensors. Dashed gray box outlines the 1L thick graphene film. Inset: schematically drawn illustration showing the cross-section of the Al2 O3 sensor along the blue line. Note that in the Au-coated sensors the Al2 O3 layer was missing. (b) and (c) Schematic illustration of the Kretschmann configuration used in the SPR measurements. During the measurements, the sensor is attached to the prism with the graphene layer on the opposite side of the incident light (k). (b) When the projected wave vector (k x ) of the incident light does not match the wave vector of surface plasmon (k SP ), no excitation occurs. (c) However, at a certain incident light angle (θ), the projected wave vector of the incident light matches the wave vector of surface plasmons, which depends on the wavelength of light and the dielectric properties of the prism ε0 , metal layer ε2 , and the surrounding medium ε1 . coatings (Au surface and Au surface Al2 O3 layer) were used to examine the effect of the sensor surface material on the measurement results. After each transfer process, SPR measurements were performed in Kretschmann configuration [see Figs. 1(b) and 1(c)] using a BioNavis MP-SPR Navi 200-L apparatus equipped with 670 and 785 nm light sources. The measurements were performed at 25°C temperature in ambient air. The measurement beam spot is approximately 0.5 mm in diameter, from which the information is averaged. All the samples were measured as a reference before the graphene deposition and then measured again after each consecutive layer deposition. The produced angular spectra were then analyzed with the method described in the next section of this work for the thickness and optical information. Raman measurements were also performed by using a confocal Raman microscope (WITec alpha 300R) equipped with a frequency-doubled Nd:YAG green laser (λ 532 nm) in order to estimate the quality of transferred graphene films. The spectra were acquired at room temperature in a backscattering geometry using a 100 × microscope objective lens. The excitation power was 1 mW. In addition, AFM measurements were performed with NT-MDT NTegra Prima apparatus to estimate the height of the transferred graphene layers. AFM imaging was performed in semi-contact mode. The maximum scan area of the apparatus was 13 μm × 13 μm. Research Article Vol. 3, No. 2 / February 2016 / Optica 3. SURFACE PLASMON RESONANCE PRINCIPLE The permittivity ε and the refractive index ñ of materials in their complex forms are ε ε 0 iε 0 0 ; (1) ñ n ik; (2) where ε 0 and ε 0 0 and n and k are the real and imaginary parts of the complex permittivity and complex refractive index, respectively. Permittivity and refractive index have the following relationships: pﬃﬃﬃ ñ ε; (3) ε n2 k2 : (4) In order to obtain the complex refractive index (and also the thickness) of the transferred graphene layer from the measured permittivity, surface Plasmon resonance measurements were performed recording the reflected light intensity as a function of incident light angle [as shown in Figs. 1(b) and 1(c)]. Surface plasmons are particle waves of the free electron plasma on a metal surface, which can be excited by p-polarized light under the resonance condition [see the difference in Figs. 1(b) and 1(c)]. A theoretical description of the resonance condition can be obtained by solving the Maxwell equations for a multilayer optical system , which provides the following mathematical solution for the resonance condition: rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ω pﬃﬃﬃﬃﬃ ω ε1 ε2 ε0 sin θ ; (5) c c ε1 ε2 where ω is the angular frequency of light, c is the speed of light in vacuum, and ε0 , ε1 , and ε2 are the permittivities of the prism, SPR metal layer, and the adjacent medium, respectively. As seen from Eq. (5), measurement of only the SPR angle is not sufficient for the unique determination of the complex permittivity and the thickness of the material. Similar reasoning was presented in Ref.  which claimed that, in addition to the SPR angle detection, another independent observable is necessary for unique determination of the complex refractive index of graphene. However, in addition to the location of the SPR angle, the shape of the spectrum also contains information regarding the material properties. In fact, the attenuated total reflection intensity (TIR angle) data (which was used as a second independent variable in Ref. ) can also be found from the measured SPR curves. Therefore, in this work, the complex permittivity and thickness of the graphene were obtained simultaneously by solving a general problem for a multilayer system. In practice, this is performed by BioNavis LayerSolver software, which fits the solution of Maxwell equations for a multilayer optical system to the measured reflectance spectrum obtained in Kretschmann configuration using a transfer matrix formalism of 2 × 2 matrices . To increase the precision of the measurement, background scans and fits for the noncoated SPR sensors were performed before deposition. The optical information obtained from these fits is provided in the Supplement 1. 4. RESULTS AND DISCUSSION A. Raman Scattering Prior to the SPR measurements, transferred graphene films were examined by Raman scattering measurements to verify the quality 153 of the transfer process. The Raman scattering measurement results are shown in Fig. 2. The spectra show three different Raman peaks in addition to the fluorescence signal from the Bionavis SPR sensor, which has been subtracted from all the shown spectra. Raman peaks located at the wavenumber of about 1335, 1580, and 2670 cm−1 can be attributed to D-, G-, and 2D peaks of graphene, thereby verifying that graphene has been transferred onto the SPR sensor. These graphene Raman peaks originate from the in-plane lattice vibrations and have been reported to occur from the A1g phonons, E2g phonons, and the overtones of A 1g phonons of graphene, respectively [17,42]. Observation of the D-peak in Raman measurements requires the presence of defects inside the graphene layer for its activation . Therefore, the intensity of the D-peak can be used as a measure of defect density inside the graphene layer (i.e., the lower the intensity the smaller the defect density) . As observed, the D-peak intensity increases with the increasing number of transfer processes which can be attributed to the different types of defects caused by the transfer processes. The presence of defects after the transfer process is expected as the wet transfer processes always affect the quality of the graphene layers . For instance, the transferred graphene layer contains wrinkles and cracks whose density increases near the edges of the transferred graphene layer (discussed later in this work). However, despite the slight increase in the Dpeak intensity, the intensity level is still low in all the samples, which implies that the quality of the transferred graphene layers is good on the SPR sensors. Lastly, it is worth noting that the Raman spectra of the graphene layer on the copper growth template is significantly noisier than the spectra of the rest of the samples. The difference in the noise level is due to the increased fluorescence signal from the copper substrate. To gather information from the 2D and G peaks, we fit a Lorenzian line shape to each Raman peak. Figures 2(b) and 2(c) show the location of the 2D peak and the intensity ratio between the G and 2D peaks as a function of the number of transfer processes. From this, we observe that 2D peaks at 2666 cm−1 , 2676 cm−1 , and 2685 cm−1 for the 1L, 2L, and 3L thick samples, Fig. 2. (a) Raman spectra of transferred graphene layers on Bionavis Al2 O3 -coated SPR sensors: as-grown on Copper (green curve), 1-layer (1L) graphene on SPR sensor (blue curve), 2-layer (2L) graphene on SPR sensor (magenta curve), and 3-layer (3L) graphene on SPR sensor (red curve). The fluorescence background has been subtracted from the measured Raman spectra for easier comparison. (b) Integrated intensity ratio between 2D and G peaks and (c) the 2D Raman peak position as a function of the number of transfers. Research Article Vol. 3, No. 2 / February 2016 / Optica 154 Fig. 3. SPR curves on [(a) and (c)] Al2 O3 and [(b) and (d)] Au sensors. The fits (dashed red curves) have been performed separately for each measurement. The laser excitation wavelength is 670 nm in (a) and (b) and 785 nm in (c) and (d). respectively, redshift. The redshift of 2D peak is 19 cm−1 from 1 to 3 layers [Fig. 2(c)], and thus is similar to the behavior reported for micromechanically exfoliated graphene flakes with increasing graphene flake thickness . The intensity ratio between the G and 2D Raman peaks, on the other hand, increases from 0.42 to 1.78 with increasing number of layers [Fig. 2(b)], also comparable to the behavior observed in Ref.  for different graphene flake thicknesses. These results imply that the graphene layer thickness increases with increasing number of graphene transfers and is therefore expected. B. Complex Refractive Index Measurement Using Surface Plasmon Resonance The optical constants of transferred graphene films were then characterized by SPR. Examples of SPR curves of the transferred graphene layers and the reference of bare Al2 O3 and bare Aucoated sensors are presented in Fig. 3. The SPR peaks show strong shifts on both sensors. For instance, the resonance peak (black curve) of the pure Al2 O3 sensor measured using 670 nm laser for excitation is at 44.58°, while for 1L (blue curve), 2L (cyan curve), and 3L (green curve) graphene samples it is at 44.93°, 45.19°, and 45.5°, respectively. For a repetition experiment of a different graphene batch on a different sensor, the background was 44.64° and 1L was 44.98° (See Supplement 1). As expected, the SPR angle difference between the different sensors for both the background and the monolayer graphene is extremely small (i.e., <0.1°), proving the good repeatability of the SPR-based characterization method for large area samples. Furthermore, the SPR peak shift is almost 1°/nm in both cases (assuming that the CVD graphene layer thickness is 0.335 nm), and therefore almost ten times larger than that of ∼0.15°∕nm for Langmuir–Blodgett (LB)-deposited stearic acid monolayers  and nanofibrillar cellulose film . This large SPR angle shift in graphene is due to the significantly higher refractive index of graphene compared to that of the organic layers [26,27]. The results from the SPR angle comparison are listed in Table 1. On the other hand, the resonance peak of the sample with graphene layer on the Au sensor locates at 43.12° and shifts slightly less than 0.6°/nm for the same incident wavelength. Therefore, the Al2 O3 sensor gives a better contrast (change of SPR peak) for the deposited graphene layer. To accurately obtain the graphene refractive index and the layer thickness (which will be discussed in the next section of this work) from the SPR results, we carried out the multiple-wavelength method analysis. Thus, the SPR measurements were also performed using a 785 nm light for excitation [shown in Figs. 3(c) and 3(d)]. Reference  raised a question as to whether the SPR method is able to uniquely distinguish the complex RI values of extremely thin layers like graphene. However, based on the SPR spectra shown in Fig. 3, this is not the case as all the shown SPR spectra are distinguishable and result in unique fitting results. Indeed, all the experimental results fit well with the theoretical simulation (dashed red lines) obtained with the method described earlier. Therefore, it seems that the experimental observations in Ref.  (performed from the SPR angle data alone) might have resulted from a significantly lower angular resolution, higher noise than that obtained from a commercial dedicated SPR instrument Table 1. SPR Angle Shifts of Various Materials Material Graphene on Al2 O3 sensor Graphene on Au sensor Stearic acid monolayer Nanocrystalline cellulose Lipid bilayers (SiO2 sensor) SPR Angle Shift (°/nm) Reference ∼1 ∼0.6 ∼0.13 ∼0.15 ∼0.2 This work This work    Research Article Vol. 3, No. 2 / February 2016 / Optica with a angular step resolution of ∼0.005°, and from the fact that their SPR data excluded the TIR region of the spectrum (i.e., the angular range between 40° and 42° of the presented spectra in Fig. 3). Due to these reasons, it was possible with the given method to uniquely deduce the complex RI of graphene layers on both sensors from a single measurement. The obtained optical constants are presented in Table 2. SPR measurement reveals that the RI of graphene on the Al2 O3 sensor is 3.135 for 1L graphene and about 3.75 for 2L and 3L graphene samples at 670 nm. Furthermore, the extinction coefficient (k) of 1L graphene is 0.897 at 670 nm, while for 2L and 3L graphene samples it decreases to 0.801 and 0.800, respectively. Moreover, comparable values for RI and extinction coefficient to the values measured with 670 nm laser are obtained when the SPR measurement is performed with 785 nm laser, as shown in Table 2. This indicates that RI and extinction coefficient are not changing significantly in this wavelength range. Nearly negligible excitation light dependence on the RI agrees well with the literature, which shows almost constant refractive index and slowly linearly increasing extinction coefficient with increasing wavelength in the visible wavelength range [12,13]. On the other hand, when the measurement is performed with graphene layers on the Au sensor, the values of 3.1 and 0.5 for refractive index and the extinction coefficient, respectively, are obtained for both 670 and 785 nm. It is worth noting there were slight difficulties in performing the fitting-based analysis on Au coating, and therefore the RI error margins are higher in this case. It is possible that the substrate smoothness (which differs between the Au and Al2 O3 sensors) affects the fitting analysis. As a matter of fact, in a work using spectroscopic ellipsometry, the substrate smoothness was also proposed to be the dominating factor for the higher error margins of the measured optical properties of graphene on SiO2 /silicon substrate than those measured on extremely smooth amorphous quartz substrate . Furthermore, the interaction between the Au substrate and graphene may also complicate the fitting analysis (e.g., electrons in plasmonic waves escape to graphene layers as no dielectric Al2 O3 layer exists in the Au sensors) and thus possibly contribute to the measurement error. We compare the SPR measurement results to the literature values measured by other groups using different measurement methods (listed in Table 3). As mentioned, SPR measurement reveals that the refractive index of 1L graphene on Al2 O3 sensor is 3.135 at the wavelength of 670 nm, which is larger than (but in the same magnitude with) the literature values which typically range between 2.6 and 3 [12–16,37]. However, the measured extinction coefficient of 0.897 is significantly smaller than the values commonly used in the literature. For instance, Ref.  reported an extinction coefficient value of 1.5 for a micromechanically exfoliated single-layer graphene Table 2. SPR Analysis Results of the Graphene Layers Wavelength 670 nm 785 nm 670 and 785 nm Sensor N n k n k d (nm) Change (nm) Al2 O3 1 2 3 1 2 3.135 3.750 3.750 3.1 3.1 0.897 0.801 0.800 0.5 0.5 3.132 3.750 3.750 3.1 3.1 0.897 0.801 0.800 0.5 0.5 0.82 1.10 1.56 1.07 1.38 – 0.28 0.46 – 0.31 Au 155 Table 3. Comparison between the Complex Refractive Index of Graphene Measured at 670 nm Using Different Methodsa Characterization Method n k SPR 3.135 0.897 SPR 3.1 0.5 SPR + attenuated 2.65 total reflection Spectroscopic 2.86 ellipsometry Optical contrast 3 1.27 Picometrology 2.95 1.32 Spectroscopic ellipsometry Spectroscopic ellipsometry Simulation 2.76 1.40 a 1.49 1.22 ∼2.75 ∼1.50 2.886 1.634 Fabrication Method Reference This work CVD graphene on Al2 O3 sensor CVD graphene on This work Au sensor CVD graphene a Exfoliated graphene flakes Exfoliated graphene flakes Exfoliated graphene flakes Exfoliated graphene flakes Polycrystalline CVD graphene Graphite   a    Measurement has been performed using 630 nm wavelength. using spectroscopic ellipsometry. This discrepancy could be because in the SPR measurements the incident and reflected light do not pass the sample itself but instead SPR uses the evanescent field in the measurement, so the field penetration direction is perpendicular to the substrate. As opposed to this, in the spectroscopic ellipsometry and optical contrast measurements, the measurement beam passes through the sample, so the complex RI is a component of both the planar and perpendicular RI. As the graphene is clearly an anisotropic material in the plane and perpendicular directions, it would be logical to have significant difference in the complex RI also. When compared to the graphite complex RI shown in Ref. , the RI has relatively small difference in the x-y-z directions (i.e., nx 2.86 and nz ∼ 2), but the extinction coefficient has a large difference between the x and z directions (i.e., kx ∼ 1.5 and kz ∼ 0). Therefore, it is likely that the discrepancy in the measured extinction coefficient values is larger than the discrepancy in the obtained RI values. For the 2L and 3L graphene samples, the RI increases to 3.75. This increase in RI could be attributed to the physical differences of the layers, as it is well known that exfoliated single-layer graphene has a different electrical structure than a multilayer graphene. However, compared to literature values of 2.886 and 1.634 for the RI and the extinction coefficient of bulk graphite, respectively, these values are significantly larger [12,46]. This could be a result of the anisotropy of graphene in the in-plane and perpendicular directions as discussed earlier. However, it is probably more likely that the differences originate from the different sample properties as the fabrication of the multilayer samples was performed using a wet transfer process, and thus they possess a completely different electrical and chemical structure (and also RI) compared to perfectly assembled exfoliated multilayer graphene or graphite crystals. C. Thickness Determination Using Surface Plasmon Resonance When we measure the refractive index of graphene using our proposed SPR-based method, it simultaneously reveals the graphene Research Article layer thickness (also given in Table 2). Note that the fitted thickness is set to be the same for both incident wavelengths and thus is obtained using multiple wavelength analysis. It is interesting to note that the first graphene layer has a thickness of 0.82 nm on the Al2 O3 substrate (and 1.07 nm on the Au substrate). This is larger than expected based on the literature value of a single layer of thick graphene, which is the same as the graphene– graphene layer difference in graphite (i.e., 0.335 nm ). To study this further, AFM measurements were performed to estimate the height of the 1L graphene edge (shown in Fig. 4). AFM measurements reveal that 1L graphene has a thickness of about 5 nm. This estimate is also significantly larger than the literature value of graphene thickness. As mentioned earlier, however, one typical problem encountered when the thickness of graphene is measured with AFM is that AFM systematically gives too large layer thickness values [22,23]. In addition to this, AFM studies reveal that the edge of the transferred graphene layer contains wrinkles. This is no surprise because the wet transfer process is far from a perfectly conformal process and can cause the edge of the transferred graphene layer to be thicker. Due to all these reasons, AFM is far from a perfect method to characterize the height of graphene layers and thus new direct methods like SPR measurement are needed. One explanation for the higher-than-expected 1L graphene thickness value is that the transferred graphene layer bridges gaps of the sensor surface. Indeed, the AFM-measured substrate roughness of the Al2 O3 sensor is 1.85 nm. This behavior could be explained by the fact that the wet transfer process is not conformal despite the large elasticity of the graphene. The same effect has also been shown to contribute to LB-deposited monolayers . Finally, it is also possible that the graphene spacing distance from a dielectric layer is higher than that from the graphene–graphene layer difference in graphite. If so, the typical behavior of AFM thickness results being systematically thicker than expected could also be partially explained by the same phenomenon. To gather more evidence from that hypothesis, we plot the obtained SPR thicknesses as a function of the number of transfer processes (shown in Fig. 5). We also fit a linear curve, i.e., d l × N b, to the obtained layer thicknesses in which l describes the thickness increase per each transfer process and b is a constant accounting for the possible gap between the graphene and the SPR sensor. From that curve, it can be observed that the layer thickness l increases by 0.37 nm on Al2 O3 sensor after each transfer is performed, and therefore agrees well with the reported value of 0.335 nm for the graphene–graphene layer difference in graphite. On the other hand, the graphene layer thickness increase per transfer on the Au sensor is 0.31 nm, thus also agreeing well with Fig. 4. (a) AFM image of the edge of the transferred graphene layer on the Al2 O3 sensor and (b) the side profile along the blue line. The height scale in the AFM image corresponds to a 40 nm difference. Vol. 3, No. 2 / February 2016 / Optica 156 Fig. 5. Obtained layer thicknesses as a function of the number of graphene transfers on the Al2 O3 -coated SPR sensors. the reported value of 0.335 nm for graphene–graphene layer thickness in graphite. The values for the fitting constant b are 0.42 and 0.76 nm on the Al2 O3 and Au sensors, respectively. If the gap, suggested by the nonzero value of b, is originating from the substrate roughness it should correlate with AFM measured surface roughness. However, the AFM-measured substrate roughness of the Au sensor is 0.4 nm and is therefore smaller than that (1.85 nm) of the Al2 O3 sensor. Thus, as a larger value of b is obtained from the Au sensor, it seems that substrate roughness is not contributing to the origin of the gap. On the other hand, the nonzero value of b may also be affected by the surface residues created by the wet transfer process. Nevertheless, it would then be likely that these residues would be present in the interfaces of two- and three-layer-thick samples. Therefore, the most probable explanation for the origin of the gap seems to be that the interaction strengths between the graphene layer and Al2 O3 or Au sensors are different and differ from the graphene–graphene layer interaction of graphite, thereby forcing the first graphene layer to be located further away from the sensor surface . 5. CONCLUSIONS We show that the SPR method can be used to characterize both the thickness and refractive index of graphene. The measured refractive index and the extinction coefficient values of CVD-grown graphene layers on the Al2 O3 sensor at 670 nm are 3.135 and 0.897, respectively, for 1L graphene and they differ with the common literature values, which typically range between 2.6 and 3 and between 1.2 and 1.5, respectively. This discrepancy is partially attributed to the anisotropy of graphene as the electric field penetration direction in SPR measurements is perpendicular to the substrate and therefore different from that used in more typical approaches (such as spectroscopic ellipsometry and optical contrast analysis). Furthermore, despite the small uncertainty in terms of the absolute layer thickness for the 1L thick graphene film, the SPR method can easily detect different graphene layer thicknesses and gives an increase of 0.37 nm per layer. All in all, the SPR peak shifts generated by each consecutive layer of graphene (∼1°∕nm) are almost ten-fold larger than those of organic monolayers due to the high refractive index of graphene, allowing us easily to determine the subnanometer layer thicknesses of large area samples (∼mm2 ). As a result, our results open the avenue for fast and cost-effective simultaneous characterization of the Research Article thickness and the optical constants of graphene (and other twodimensional layered materials). The presented characterization method can therefore be applied both to the graphene physical characterization as well as to the use of graphene in biosensing applications as presented earlier . Funding. Academy of Finland (284548, 285972); Seventh Framework Programme (FP7) (631610). Acknowledgment. The authors also thank Aalto University and the Micronova Nanofabrication Centre for the provision of facilities and technical support. H. J. thanks the Jenny and Antti Wihuri Foundation for the financial support. H. Y. acknowledges China Scholarship Council (CSC) for the financial support. See Supplement 1 for supporting content. REFERENCES 1. A. C. Ferrari, F. Bonaccorso, V. Fal’ko, K. S. Novoselov, S. Roche, P. Bøggild, S. Borini, F. H. L. Koppens, V. Palermo, N. Pugno, J. 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